Transverse localization of directed waves in random media

In this work we consider the propagation of directed waves in random media with a finite correlation scale in the longitudinal direction. The problem is described by a standard parabolic equation of the same type as the nonstationary Schrödinger equation describing the motion of a quantum particle in a dynamically varying random potential. Applying the path integral approach, we study perturbatively the mean intensity distribution of a pointlike source located in a random medium with inhomogeneities stretched along the propagation direction. We show that in this case the intensity is enhanced on the axis and reduced on the edges of the beam, which can be related to the phenomenon of transverse localization. The dependence of the transverse localization length on the geometry of the problem in different propagation regimes is examined. Though the language of classical waves is used, the results are valid for the quantum case as well.